Elegant Ince-Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard In...Elegant Ince-Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince-Gaussian beams and they display better symmetry between the ]nce-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince Gaussian beams are discussed.展开更多
A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their t...A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.展开更多
Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will l...Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.展开更多
We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation wi...We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue problem. We investigate the representation of the four Sturm-Liouville operators by infinite banded matrices.展开更多
Control mode for typical karst rocky desertification in Guizhou Province,China is selected as the research object.The ecological benefit,the social and economic benefit and the popularization prospect of mode are sele...Control mode for typical karst rocky desertification in Guizhou Province,China is selected as the research object.The ecological benefit,the social and economic benefit and the popularization prospect of mode are selected as evaluation indices.Evaluation index system of control modebenefits for karst rocky desertification is established.The Dingtan mode and the Wangjiazhai-Yangchangdong small watershed control mode are se-lected as evaluation objects.Preliminary assessment on the two modes are carried out by Analytic Hierarchy Process,grading evaluation,and com-prehensive evaluation method.Result shows that comprehensive score of Dingtan mode is 3.81,which is higher than the score of Wangjiazhai-Yangchangdong small watershed control mode(3.11).In the aspects of ecological benefit and social and economic benefit,Dingtan mode(4.83and 3.258) is superior than the Wangjiazhai-Yangchangdong small watershed control mode(3.38 and 2.531).In the aspect of popularization pros-pect of mode,score of Dingtan mode(3) is lower than that of Wangjiazhai-Yangchangdong small watershed control mode(3.333).Therefore,theevaluation index system has certain science and offers reference and guidance for the karst rocky desertification control in southwest China.展开更多
A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell’s mode in an elliptic coordinate system,and their trans...A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell’s mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schro¨dinger equation.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10904041 and 10674050)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20094407110008)the Specialized Research Fund for Growing Seedlings of the Higher Education in Guangdong Province,China (Grant No.C10087)
文摘Elegant Ince-Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince-Gaussian beams and they display better symmetry between the ]nce-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince Gaussian beams are discussed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11074080 and 10904041)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20094407110008)the Natural Science Foundation of Guangdong Province of China (Grant No. 10151063101000017)
文摘A novel class of optical breathers, called elegant Ince-Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell＇s mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear SchrSdinger equation.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51379005 and 51009093)
文摘Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.
基金Key Research Program of Guangdong Province (Grant No. 2002C20703) and Key Research Program of Guangdong Provincial Department ofForestry (Grant No. 2002-12)
文摘We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue problem. We investigate the representation of the four Sturm-Liouville operators by infinite banded matrices.
基金Supported by the Special Project for High-level Talents of Guizhou Province (TZJF-2008.No.22)
文摘Control mode for typical karst rocky desertification in Guizhou Province,China is selected as the research object.The ecological benefit,the social and economic benefit and the popularization prospect of mode are selected as evaluation indices.Evaluation index system of control modebenefits for karst rocky desertification is established.The Dingtan mode and the Wangjiazhai-Yangchangdong small watershed control mode are se-lected as evaluation objects.Preliminary assessment on the two modes are carried out by Analytic Hierarchy Process,grading evaluation,and com-prehensive evaluation method.Result shows that comprehensive score of Dingtan mode is 3.81,which is higher than the score of Wangjiazhai-Yangchangdong small watershed control mode(3.11).In the aspects of ecological benefit and social and economic benefit,Dingtan mode(4.83and 3.258) is superior than the Wangjiazhai-Yangchangdong small watershed control mode(3.38 and 2.531).In the aspect of popularization pros-pect of mode,score of Dingtan mode(3) is lower than that of Wangjiazhai-Yangchangdong small watershed control mode(3.333).Therefore,theevaluation index system has certain science and offers reference and guidance for the karst rocky desertification control in southwest China.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11074080 and 10904041)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20094407110008)the Natural Science Foundation of Guangdong Province of China (Grant No. 10151063101000017)
文摘A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell’s mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schro¨dinger equation.
